Question

$(64{)}^{-\frac{1}{2}}-(-32{)}^{-\frac{4}{5}}=?$

• A. $\frac{1}{8}$
• B. $\frac{3}{8}$
• C. $\frac{1}{16}$
• D. $\frac{3}{16}$

Answer 1

Answer: (C)

$\frac{1}{16}$

$(64{)}^{-\frac{1}{2}}-(-32{)}^{-\frac{4}{5}}$
$={\left(2^6\right)}^{\frac{-1}{2}}-{\left((-2{)}^5\right)}^{\frac{-4}{5}}$
$=(2{)}^{-\frac{6}{2}}-(-2{)}^{-\frac{4\times 5}{5}}$
$=(2{)}^{-3}-(-2{)}^{-4}$
$\frac{1}{8}-\frac{1}{16}=\frac{1}{16}$
Answer $C$ option, $\frac{1}{16}$